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Title: On the Convergence of an Implicit Iteration Scheme for a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces
Authors: Banerjee, Shrabani
Choudhury, Binayak S.
Keywords: Implicit iteration process with errors
asymptotically nonexpansive mapping
uniformly convex Banach space
common fixed point
Condition (B )
Opial’s condition
Kadec-Klee property
Issue Date: 2008
Publisher: Vidyasagar University , Midnapore , West-Bengal , India
Series/Report no.: Journal of Physical Science;Vol 12 [2008]
Abstract: In this paper we define a new implicit iterative process with errors in a real Banach space and establish a necessary and sufficient condition for the strong convergence of the iteration to a common fixed point for the case of a finite family of asymptotically nonexpansive mappings in a arbitrary real Banach space. Also we study the weak and strong convergence results of this implicit iterative scheme for the same family of mappings in the setting of a uniformly convex Banach space. Our results extend and generalize a number of existing results.
Description: 65-82
ISSN: 0972-8791 (Print)
Appears in Collections:Journal of Physical Sciences Vol.12 [2008]

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